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CBSE Class 12-science Answered

sir/madam
Asked by Nevin | 17 Aug, 2012, 08:47: AM
answered-by-expert Expert Answer

x: number of ounces of Food X
y: number of ounces of Food Y

Since I can't use negative amounts of either food, the first two constrains are the usual ones: x > 0 and y > 0. The other constraints come from the grams of fat, carbohydrates, and protein per ounce:

fat:        8x + 12y > 24
carbs:  12x + 12y > 36
protein:  2x +   1y >   4

Also, the maximum weight of the food is five ounces, so:

x + y < 5

The optimization equation will be the cost relation C = 0.2x + 0.3y

Draw the required graph, you will find that the corner points are (0, 4), (0, 5), (3, 0), (5, 0), and (1, 2), The cost will be minimum at (3, 0).

The minimum cost will be $0.60 per ounce, using three ounces of Food X only.

Answered by | 17 Aug, 2012, 03:31: PM

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